Health effects as a result of the accident at the Chernobyl nuclear power plant occurred in 1986 are considered in the paper. Wrong prognosis of the health effects with respect to mortality and morbidity among the population exposed to low radiation doses is shown. Linear relationship between thyroid cancer cases and dose to thyroid ranged from 0.2 to 4.0 Gy is considered. During the fifteen years following the accident no cases of acute and chronic radiation sickness have been revealed. Also, exposures to low radiation doses did not result in excess of malignant tumors among population. In some cases the outcomes of acute radiation sickness were as follows: radiation damages to the skin, cancer cataracts, development of oncopathology.